catalogue
Brief introduction of lever
Definition of lever
The essence of lever
equilibrium condition
Classification of lever
Lever in life
Investment leverage
Lever in management
Leverage ratio
Leverage effect in finance
Leverage effect in futures
Leverage effect of warrants
Leverage effect in foreign exchange transactions
Brief Introduction of Archimedes' Ideal Lever
Definition of lever
The essence of lever
equilibrium condition
Classification of lever
Lever in life
Investment leverage
Lever in management
Leverage ratio leverage effect
Leverage effect in finance, leverage effect in futures, leverage effect in warrants, leverage effect in foreign exchange transactions Archimedes' Ideal introduces leverage in the book.
Edit the introduction of leverage in this paragraph.
A hard rod that can rotate around a fixed point under the action of force is called a lever. According to the needs of life, the lever can be made straight or curved. Archimedes [1] put forward the lever principle for the first time in his book On the Balance of Plane Graphics. He first regarded some empirical knowledge in the practical application of leverage as "self-evident axioms", and then from these axioms, he used geometry and strict logical argumentation to draw the principle of leverage. These axioms are: (1) If equal weights are hung at both ends of a weightless bar at the same distance from the fulcrum, they will be balanced; (2) Hang unequal weights at the same distance from the fulcrum at both ends of the weightless bar, and the heavy end will fall; (3) Hang an equal weight at both ends of the weightless bar with different distances from the fulcrum, and the far end will incline downward; (4) The function of one weight can be replaced by the function of several evenly distributed weights, as long as the position of the center of gravity remains unchanged. On the contrary, several evenly distributed weights can be replaced by a weight hanging from their center of gravity; The center of gravity of the graph is also distributed in a similar way ... It is from these axioms that Archimedes discovered the lever principle on the basis of the theory of "center of gravity", that is, "when two heavy objects are in equilibrium, their distance from the fulcrum is inversely proportional to their weight." Archimedes' research on lever not only stays in theory, but also makes a series of inventions according to this principle. It is said that he used to make the mast boat parked on the beach smoothly launch with the help of lever and pulley block. In the battle to defend Syracuse from the Roman navy, Archimedes used the lever principle to make long-range and short-range catapults, and used them to launch various missiles and boulders to attack the enemy, which once made the Romans stay outside Syracuse for three years. Incidentally, there are also records about leverage in the history of our country. Mohist school in the Warring States period once summarized this law, and there are two special records about the principle of leverage in Mohist book. These two articles elaborated the balance of leverage very comprehensively. There are equal arms and unequal arms inside; Some change the weight of both ends to make it biased, and some change the length of the two arms to make it biased. Such a record is also very valuable in the history of world physics.
Edit the definition of lever in this paragraph.
Lever is a simple machine. A hard rod that can rotate around a fixed point under the action of force is a lever. The lever is not necessarily straight or curved, but it must be guaranteed in the physics book.
This is a hard stick. Seesaws, scissors, wrenches and crowbars are all levers. The pulley is a deformed lever, the crown block is an equal arm lever, and the moving pulley is the lever principle that the power arm is twice as large as the resistance arm.
Edit the properties of the lever in this paragraph.
The fixed point around which the lever rotates is called fulcrum, the force that makes the lever rotate is called force, and the force that hinders the lever from rotating is called resistance. When the force and resistance cancel each other's rotation effect, the lever will be in a state of balance, which is called lever balance, but lever balance is not the balance of force. When the lever is balanced, it remains stationary or rotates at a constant speed. The straight line passing through the point of force in the direction of force is called the vertical distance L 1 from fulcrum o to force line F 1, and the vertical distance L2 from fulcrum o to resistance F2 of force arm is called the lever balance condition of resistance arm: force× force arm = resistance× resistance arm or written as f/kloc-0 /× l/kloc-0.
Edit the balance condition of this paragraph.
When using a lever, if the lever is stationary or rotates at a uniform speed around the fulcrum, then the lever is in a state of balance. Power arm× power = resistance arm× resistance, that is, L 1F 1=L2F2, which can evolve into F2/F 1=L 1/L2. The balance of lever is not only related to force and resistance, but also to the point and direction of force. If the power arm is n times that of the resistance arm, then the power is the 1/n lever principle of the resistance.
The longer the power arm, the more labor-saving, and the longer the resistance arm, the more effort. Hard rods save distance. Equal arm lever is neither labor-saving nor laborious. You can use it to weigh. For example; Balance.
Edit the classification of levers in this section.
One: the fulcrum is between the strength point and the resistance point. It is called the first lever. It may be labor-saving or laborious, mainly depending on the position of the fulcrum or the length of the arm. For example: seesaws, scissors, paddles, trolleys (used to transport heavy objects, such as gas tanks), shoehorns, tower cranes, pry wrenches, etc. The second category: the resistance point is between the strength point and the fulcrum. It is called the second lever. Because the power arm is always larger than the resistance arm, it is a labor-saving lever. For example: nut clips, doors, staplers, diving boards, wrenches, bottle openers (for beer) and trolleys (for transporting cement and bricks). Three kinds: the power point is between the fulcrum and the resistance point. It is called the third lever. The characteristic is that the power arm is shorter than the resistance arm, so this lever is more laborious, but it can save distance. Examples: tweezers, arms, fishing rods, paddles, jaws of kayaks, shovels, brooms, sticks and other appliances with one hand as the fulcrum and one hand as the power. In addition, tools such as wheel shafts are also a kind of deformation lever. Take the simplest lever crown block similar to the first one as an example. The shaft of the pulley is like a fulcrum, and the pull of the objects at both ends is like the application of force at both ends of the lever. If the pulley is a perfect circle, both the arm of force and the arm of resistance will be the radius of the circle.
The lever of editing this life.
Lever is a simple machine; You can use a strong stick (preferably not bent, very light) as a lever. In the picture above, the square represents the weight, the circle represents the support point, and the arrow represents the purpose. Did you get a look at him? In the lever right lever experiment
The side lower lever is an equal arm lever; The second is that the center of gravity is in the middle, and the power arm is larger than the resistance arm, which is a labor-saving lever; The third is that the power point is in the middle, and the power arm is smaller than the resistance arm, which is a laborious lever. Labor-intensive tools, such as scissors, nails, nail puller ... levers may be labor-intensive, labor-intensive or neither. It depends on the distance between the force point and the fulcrum: the farther the force point is from the fulcrum, the more effort it takes, and the closer it is to the fulcrum, the more effort it takes; It also depends on the distance between the key point (resistance point) and the fulcrum: the closer the key point is to the fulcrum, the more labor-saving it is, and the farther it is, the more laborious it is; If the key point and the stress point are far away from the fulcrum like the crown block and the balance, it is neither labor-saving nor laborious, and it will only change the direction of the force. Bottle opener, juicer, nutcracker and other labor-saving levers ... The stress point of this lever is definitely closer to the fulcrum than the key point, so it will always be more labor-saving. If we use flower scissors (with shorter blades) and foreign cutting knives (with longer blades) to cut paper respectively, flower scissors are labor-saving but time-consuming; Cutting abroad is laborious but time-saving. 1. It takes a lot of force to cut hard objects, which shows the great resistance. Use scissors with longer power arm and shorter resistance arm. 2. Paper-cutting or cloth can cut soft objects such as paper or cloth with less force, indicating that the resistance is small, and at the same time, in order to speed up the cutting speed, the knife edge should be longer. Scissors with short arm and long arm. 3. When pruning branches, on the one hand, the branches are hard, which requires the power arm of scissors to be longer and the resistance arm to be shorter; On the other hand, in order to speed up the trimming and trim neatly, the cutting edge is required to be longer. Use scissors with longer power arm, shorter resistance arm and longer blade. The balance is a special lever, and its force arm and resistance arm are the same.
Edit the leverage of this investment.
The attraction of leverage warrants is that they can be small or large. Investors only need to invest a small amount of money and have the opportunity to win similar or even higher returns than investing in stocks. However, investors often confuse the leverage ratio of warrants with the actual leverage ratio when choosing warrants. What's the difference between them? What should I look at when investing? If you want to know whether these two terms are confused, you can ask a question: suppose there are two warrants for the same share, the leverage of warrant A is 6.42 times, while the leverage of warrant B is 16.22 times. When the stock price goes up, which one goes up more? Many people may choose answer B. In fact, it depends on the potential increase of warrants, and the actual leverage ratio of warrants should be compared rather than the leverage ratio. Due to the lack of enough information, we can't get the answer from this question. Leverage ratio = stock spot price ÷ (warrant price x share conversion ratio) Leverage ratio reflects the cost ratio of investment stocks relative to investment warrants. Assuming that the leverage ratio is 10 times, it can only show that the cost of investment warrants is one tenth of that of investment stocks, but it cannot show that when stocks rise 1%, the warrant price will rise 10%. Here are two subscription cards with the same maturity date and extension range, but different exercise prices. As can be seen from the table, in terms of subscription certificates, the exercise price is higher than the positive stock price, the stock certificate price is generally low, and the leverage ratio is generally high. However, if investors use leverage to predict the potential increase of warrants, the actual performance may be disappointing. When the stock rises 1%, warrant A with leverage ratio of 6.4 times actually rises by 4.2% (instead of 6.4%), and warrant B with leverage ratio of 16.2 times actually rises by 6% (instead of 16.2%).
Edit the lever in this operation.
Refers to the law that the profit change rate is greater than the production and sales change rate because of the existence of fixed costs in the production and operation of enterprises. According to the cost behavior, in a certain range of production and sales, the increase of production and sales will generally not affect the total fixed cost, but will reduce the fixed cost of unit products, thus improving the profit of unit products and making the profit growth rate greater than the production and sales growth rate; On the other hand, the reduction of production and sales will increase the fixed cost of unit products, thus reducing the profit of unit products, so that the profit decline rate is greater than that of production and sales. Therefore, only when there is no fixed cost, can the product make the contribution gross profit equal to the operating profit, and make the change rate of profit increase or decrease synchronously with the change rate of production and sales. But this situation does not exist in reality. In this way, due to the existence of fixed costs, the profit change rate is greater than the change rate of production and sales. In management accounting and enterprise financial management, the operating profit during the planning period is often predicted according to the change rate of production and sales during the planning period. In order to quantify the operating leverage, the ratio of profit change rate to production and sales (or sales revenue) change rate is called "operating leverage coefficient" and "operating leverage rate" in enterprise financial management and management accounting, which is expressed by the following formula: the operating leverage coefficient can also be calculated by the following formula: after obtaining the operating leverage coefficient, assuming the fixed cost remains unchanged, the operating profit in the planned period can be predicted by the following formula: operating profit in the planned period = operating profit in the base period × (/kloc-). Under the action of a certain fixed cost ratio, the influence of sales volume changes on profits is called operating leverage. Because operating leverage has the most comprehensive impact on business risk, it is often used to measure the size of business risk. The size of operating leverage is generally expressed by operating leverage coefficient, that is, the ratio of EBIT change rate to sales change rate. The size of business risk is usually measured by operating leverage, operating leverage's leverage analysis chart.
The size is generally expressed by operating leverage coefficient, which is the ratio of profit change rate to sales change rate before calculating interest and income tax. First, it reflects the changing relationship between profit change and sales volume change; Second, the greater the operating leverage coefficient, the greater the role and operational risk of operating leverage; Third, the fixed cost is constant, the greater the sales volume, the smaller the operating leverage coefficient and the smaller the operating risk, and vice versa; Fourth, when sales reach the critical point of profit and loss, the operating leverage coefficient approaches infinity. Enterprises can generally reduce operating leverage and operational risks by increasing sales and reducing unit variable and fixed costs. Ways to Control operating leverage Enterprises can generally reduce the operating leverage rate and operational risk by increasing the sales amount, reducing the unit variable cost of products and reducing the proportion of fixed costs. Operating leverage can be understood from two aspects. On the one hand, it can be seen from the calculation formula of operating leverage coefficient that the marginal contribution will increase with the increase of unit price and sales volume. Operating leverage coefficient = marginal contribution/(marginal contribution-fixed cost), because the denominator has to subtract a fixed cost, and the denominator is always smaller than the numerator, so when a value is added at the same time, the increase is relatively small compared with the numerator with a larger amount. Compared with the denominator with a smaller amount, it has a larger increase, so the larger the denominator increases, the smaller the whole formula, that is, the smaller the operating leverage coefficient. For example, marginal contribution = 100, fixed cost = 20, operating leverage coefficient = 100/( 100-20) = marginal contribution = 120, and fixed cost remains unchanged, then120/
Edit the leverage ratio of this paragraph.
The attraction of warrants is that they can be small or large. Investors only need to invest a small amount of money and have the opportunity to win similar or even higher returns than investing in stocks. However, investors often confuse the leverage ratio of warrants with the actual leverage ratio when choosing warrants. What's the difference between them? What should I look at when investing? If you want to know whether these two terms are confused, you can ask a question: suppose there are two warrants for the same share, the leverage of warrant A is 6.42 times, while the leverage of warrant B is 16.22 times. When the stock price goes up, which one goes up more? Many people may choose answer B. In fact, it depends on the potential increase of warrants, and the actual leverage ratio of warrants should be compared rather than the leverage ratio. Due to the lack of enough information, we can't get the answer from this question. Leverage ratio = stock spot price ÷ (warrant price x share conversion ratio) Leverage ratio reflects the cost ratio of investment stocks relative to investment warrants. Assuming that the leverage ratio is 10 times, it can only show that the cost of investment warrants is one tenth of that of investment stocks, but it cannot show that when stocks rise 1%, the warrant price will rise 10%. Here are two subscription cards with the same maturity date and extension range, but different exercise prices. As can be seen from the table, in terms of subscription certificates, the exercise price is higher than the positive stock price, the stock certificate price is generally low, and the leverage ratio is generally high. However, if investors use leverage to predict the potential increase of warrants, the actual performance may be disappointing. When the stock rises 1%, warrant A with leverage ratio of 6.4 times actually rises by 4.2% (instead of 6.4%), and warrant B with leverage ratio of 16.2 times actually rises by 6% (instead of 16.2%).
Edit the leverage effect of this paragraph.
Leverage effect in finance
The leverage effect in finance, that is, the financial leverage effect, refers to the phenomenon caused by the existence of fixed fees. When a financial variable changes in a small range, another related variable will change in a large range. That is to say, when enterprises adopt debt financing methods (such as bank loans, issuing bonds and preferred shares), the change rate of earnings per share of common stock is greater than that of earnings before interest and tax. Because the financial expenses such as interest expense and preferred stock dividend are fixed, when the income before interest and tax increases, the fixed financial expenses per common stock will decrease relatively, thus bringing additional income to investors. The leverage effect in finance includes operating leverage, financial leverage and compound leverage. 1, operating leverage refers to the leverage effect that the change of earnings before interest and tax is greater than the change of production and sales due to the existence of fixed costs. 2. Financial leverage refers to the leverage effect that the change of earnings per share of common stock is greater than the change of earnings before interest and tax due to the existence of debt. 3. Composite leverage refers to the leverage effect that the change of earnings per share of common stock is greater than the change of production and sales due to the existence of fixed production and operation costs and fixed financial expenses.
Leverage effect in futures
The leverage effect in futures is the original mechanism of futures trading, that is, the margin system. The "leverage effect" not only enlarges the tradable volume of investors, but also doubles the risks taken by investors. Suppose a trader trades stocks or spot with a sum of 50,000 yuan, and the trader's risk is about leverage.
It's just stocks or commodities worth 50 thousand yuan. If all the funds of 50,000 yuan are used for stock index futures trading, the risks borne by traders are brought by stocks or commodities worth about 500,000 yuan, which magnifies the risks by about ten times, and of course the corresponding profits are also magnified by ten times. It should be said that this is not only the fundamental risk source of stock index futures trading, but also the charm of stock index futures trading
Leverage effect of warrants
The leverage effect of warrants is determined by the product characteristics of warrants. Assume that the current price of the underlying stock is 65,438+00 yuan, the exercise price of the underlying stock warrant is 65,438+02 yuan, and the market price of the warrant (assuming the warrant conversion ratio is 65,438+0: 65,438+0) is 0.5 yuan. If investors buy warrants, it is equivalent to investing 12 yuan in the underlying stock at the cost of 0.5 yuan. If the underlying stock rises to 15 yuan in the future, its yield (excluding transaction costs) is: investment warrant yield = (15-12-0.5)/0.5 = 50. Its rate of return = (15-10)/10 = 50% Because of the leverage effect of warrants, if investors correctly judge the market outlook of the underlying assets, the return on investment of warrants will often be much higher than that of the underlying assets. On the contrary, the warrant investment will be wiped out. Of course, if investors buy the same amount of underlying assets instead of warrants and hold the rest in cash, the risk will be less, because the biggest loss for investors is not too high royalties.
Leverage effect in foreign exchange transactions
The leverage effect of foreign exchange transactions is also quite common in China. Traders can trade 65,438+00 to 65,438+000 times as long as they pay 65,438+0% margin. What's more, the margin is as low as 0.5%, and the transaction is as high as 200 times. Because leveraged foreign exchange transactions have low capital requirements for investors, they can hold positions indefinitely; Coupled with flexible trading methods, it has attracted many investors. Because of the time difference between Asian market, European market and American market, it has become a 24-hour global foreign exchange market. No matter where investors are, they can participate in any market transactions at any time. The foreign exchange market is a market without time and space barriers. Leveraged foreign exchange trading seems to be a high-risk financial leveraged trading tool. Because the participants in margin trading only pay a small percentage of the margin, the normal fluctuation of foreign exchange prices is magnified several times or even dozens of times, and the gains and losses brought by this high risk are amazing. On the other hand, the daily turnover of the international foreign exchange market can reach more than 1 trillion dollars, and many international financial institutions and funds participate in it. The economic policies of various countries change at any time, and all kinds of unexpected events occur from time to time, which may be the reasons for the large fluctuations of exchange rates. Large organizations employ a large number of human resources, obtain first-hand information from various channels, and the investment team uses the analysis results to make profits in real time. Although the amount of margin for leveraged foreign exchange trading is small, the actual funds used are huge, and the foreign exchange price fluctuates greatly every day. If investors misjudge the trend of foreign exchange, they will easily be wiped out. In case of unexpected market conditions, if measures are not taken in time, not only the principal will be completely lost, but also the price difference may be added. Investors must not take it lightly. When determining the leverage ratio, we must understand the risks.
Edit this passage from Archimedes' Ideal.
Archimedes studied mechanics and applied it to the mechanical design of levers and pulleys. It is said that in order to publicize his research results, he boasted: "Give me a fulcrum and I can move the earth." Although he didn't move the earth, he moved Archimedes' ideal with a pulley.
Big ship. The fulcrum is 65438+ 100000 meters away from the earth. If an object can lift 60kg on the earth, it needs to be 65,438+0x65,438+0065,438+08 (65,438+08 power) kilometers away from the fulcrum to move the earth. The mass of the earth is 6x65,438+0024 (to the 24th power). That is1a.u. =1.5x108 (8th power) km, and a light year is the distance traveled by light in one year,1l.y. ≈ 9.5x101.